A couple deposits $19,000$⁢19,000 into an account earning 3%3% annual interest for 2020 years. Calculate the future value of the investment if the interest is compounded monthly. Round your answer to the nearest cent.

To calculate the future value of an investment compounded monthly, we use the compound interest formula:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

Where:
- $ A $ is the future value of the investment
- $ P $ is the principal amount (initial investment), $ P = 19,000 $
- $ r $ is the annual interest rate, $ r = 0.03 $ (3%)
- $ n $ is the number of times the interest is compounded per year, $ n = 12 $ (monthly compounding)
- $ t $ is the time in years, $ t = 20 $

Now, substitute the given values into the formula:

\[
A = 19,000 \left(1 + \frac{0.03}{12}\right)^{12 \times 20}
\]

Simplify step by step:

1. $ \frac{0.03}{12} = 0.0025 $
2. $ 12 \times 20 = 240 $
3. $ A = 19,000 \left(1 + 0.0025\right)^{240} = 19,000 \left(1.0025\right)^{240} $
4. $ \left(1.0025\right)^{240} \approx 1.819396 $

Now calculate the future value:

\[
A \approx 19,000 \times 1.819396 \approx 34,568.52
\]

So, the future value of the investment is approximately **$34,568.52**.

Would you like more details or have any questions about this calculation?

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Here are 5 related questions for further practice:
1. What would the future value be if the interest was compounded quarterly instead of monthly?
2. How would the future value change if the interest rate was 5% instead of 3%?
3. What is the impact of doubling the investment period from 20 years to 40 years?
4. What is the total interest earned after 20 years?
5. How much would you need to invest to achieve a future value of $50,000 in 20 years at the same interest rate?

**Tip**: The more frequently interest is compounded, the higher the future value will be, as interest is applied more often.

A couple deposits $19,000 into an account earning 3% annual interest for 20 years. Calculate the future value of the investment if the interest is compounded monthly. Round your answer to the nearest cent.

Learn how to calculate the future value of a $19,000 investment over 20 years at an interest rate of 3% compounded monthly. This guide provides a step-by-step solution using the compound interest formula, ideal for students in Grades 9-12.

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